Question

A uniform sheet of metal in the shape of a hemisphere of radius 1 m is used as a sign. The hemisphere has a mass of 200 kg and is suspended by two vertical wires attached to points along its horizontal diameter. One wire is attached to the left end of the diameter and the other is attached to a point three-quarters of the way to the other end. What is the tension in each wire? A ladder 10 m long and weighing 200 N is placed against a frictionless wall with its base 6 m from the bottom of the wall. If the coefficient of static friction between the floor and the how far up the ladder is 0.2 how far up the ladder can a man weighing 800 N climb before the base of the ladder starts to slip? A gate of height 1 m, length, 2 m, and weight 400 N is hinged at points A and B as shown in the figure below. The tension T in a support cable making an angle of 30 degree is adjusted until the horizontal force at hinge A is zero. Find (a) find the tension T, (b) the horizontal component of the force exerted on the gate by hinge B, and (c) the sum of the vertical components of the forces exerted on the gate by hinges A and B.

#4 please

Answer 1

using equilibrium of force in vertical direction

T₁ + T₂ = mg

T₁ + T₂ = 200 x 9.8 = 1960 N

T₁ + T₂ = 1960 eq-1

using equilibrium of torque about B

T₁ (AB) = T₂ (BC)

T₁ (r) = T₂ (r/2)

T₂ = 2 T₁ eq-2

using eq-1 and eq-2

T₁ + 2 T₁ = 1960

T₁ = 653.33 N

using eq-2

T₂ = 2 T₁ = 2 x 653.33 = 1306.67 N